Transportation-burnup coupling calculation method based on self-adaptive burnup step length division

Abstract

The invention provides a transport-burnup coupling calculation method based on adaptive burnup step size division, and belongs to the field of reactor physical computation.The method comprises the steps that an explicit relation model of average neutron flux density and burnup step size is established, and convergence criteria are set to achieve optimal step size estimation; and constructing an iterative solution model based on a strict neutron-flux density expression, and determining an optimal burn-up step length through a convergence criterion. Finally, convergence verification is adopted to ensure the constancy of neutronics parameters in the current step length, and the numerical error is controlled within a permissible range; and by comparing the burnup results of the optimal step length and the initial step length, the influence of the step length on the calculation precision is quantitatively evaluated. The method has the core advantages that on the premise that calculation precision is guaranteed, self-adaptive division of the burnup step length in the whole life period is achieved, the number of times of transport-burnup coupling calculation is reduced, only one-time transport calculation is needed in each burnup step length, the transport-burnup coupling iteration frequency is effectively reduced, and the overall calculation efficiency is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of reactor physics calculation, specifically relating to a transport-burnup coupling calculation method based on adaptive burnup step size partitioning. Background Technology

[0002] Transport-burnup coupled computation, a core technology in reactor physics analysis, aims to significantly improve computational efficiency by minimizing the frequency of transport calculations while maintaining rigorous computational accuracy and numerical stability. Existing coupled computation methods mainly include substep methods, various prediction-correction methods, higher-order coupling methods, and generalized perturbation theory methods. These methods can improve the accuracy and efficiency of burnup calculations to some extent through different numerical computation strategies. However, most of these methods extrapolate or interpolate neutronics parameters at the start, midpoint, and end points within a single burnup step, requiring two transport calculations and multiple burnup calculations. This contributes limitedly to improving the efficiency of high-fidelity burnup calculations and fails to meet the computational demands of modern reactor fine-grained analysis. Based on the analysis of actual physical processes in high-fidelity burnup calculations, reactor burnup involves complex time-space multi-scale problems. The nuclear density evolution of various nuclides within the reactor follows a set of highly nonlinear spatiotemporal coupling equations, and the strong coupling relationships between various neutronics parameters pose significant numerical challenges to accurate solutions. A crucial assumption commonly used in current burnup calculation frameworks is that neutron parameters remain constant within the burnup step. However, this assumption deviates from physical reality. As the burnup depth increases, key parameters such as core nucleus density and power distribution continuously change, and the assumption of fixed neutron parameters inevitably introduces significant computational errors. The burnup step division strategy has become a critical bottleneck restricting the efficiency and accuracy of high-fidelity burnup calculations. Shorter step divisions can effectively improve computational accuracy and numerical stability, but significantly increase computational time costs; while longer step divisions can greatly reduce the number of transport calculations, the drastic changes in neutron parameters within the step often lead to severe loss of computational accuracy and may even cause numerical instability. Therefore, a reasonable burnup step division method is needed to achieve an optimal balance between computational accuracy and efficiency while minimizing the errors introduced by the assumption of constant neutron parameters within the step. Summary of the Invention

[0003] The technical problem this invention aims to solve is that existing transport-fuel consumption calculation methods require empirical division of the fuel consumption step size. As the fuel consumption depth increases, the number of transport-fuel consumption coupling calculations also increases. Furthermore, within each fuel consumption step size, two transport calculations and multiple fuel consumption calculations are often required, which offers very limited improvement in efficiency for high-fidelity fuel consumption calculations. Therefore, this invention proposes a transport-fuel consumption coupling calculation method based on adaptive fuel consumption step size division. This method can reduce the frequency of transport-fuel consumption coupling calculations while maintaining calculation accuracy throughout the entire coupling calculation process, saving significant computation time and costs.

[0004] To achieve the above-mentioned objectives, the present invention is implemented through the following technical solution: a transport-fuel consumption coupling calculation method based on adaptive fuel consumption step size partitioning, comprising the following steps: S1: Based on the evaluation database, obtain the fission energy, capture energy and decay energy of each nuclide; S2: Based on thermal power and available energy conversion, construct explicit equations for neutron flux density and burnup step size; S3: Determine the custom burnup step size based on the explicit equation of neutron flux density and burnup step size; S4: Determine if the current step size satisfies the rough estimate of the optimal step size for fuel consumption calculation. If the current fuel consumption step size does not reach the rough estimate of the optimal step size, then adjust the step size and proceed to S3; If the current fuel consumption step size reaches the rough estimate of the optimal step size, then proceed to S5; S5: Pass the current burnup step size and neutron flux density, and construct the iterative form of the neutron flux density; S6: Determine if the current step size satisfies the optimal step size for fuel consumption calculation: If the current fuel consumption step size has not reached the optimal step size, adjust the step size and proceed to S5; If the current fuel consumption step size reaches the optimal step size, proceed to S7; S7: Calculate the time integral average of neutronics parameters at the current fuel consumption step; S8: Determine whether the constant neutronics parameters within the burnup step meet the required computational accuracy. If the neutronics parameters remain constant within the current fuel consumption step and the required calculation accuracy is not met, then adjust the step size and proceed to S3; If the neutronics parameters remain constant within the current burnup step and meet the required computational accuracy, then the current burnup step is output.

[0005] Preferably, the evaluation database in S1 uses ENDF / B-VIII.0 or JENDL-5.

[0006] Preferably, in S2, an explicit equation is constructed for the neutron flux density and the burnup step size; this includes the following steps: S201: The relationship between thermal power and available energy power is as follows: (1) In the formula: Thermal power; This refers to the fission power. The decay power; For capturing power; S202: Neutron flux density required to solve the burnup equation The neutron flux density is calculated after converting thermal power into usable energy. The relationship between thermal power and available energy is as follows: (2) In the formula: Thermal power; The decay power; Neutron flux density; For fission energy, To capture energy; S203: For each available energy, the fission energy, capture energy, and decay energy of each nuclide obtained from the database are used to obtain: (3) (4) (5) In the formula: , , They are nuclides i The recoverable energy from each fission, capture, and decay; , , Different nuclides i Single-group fission, trapping cross section, and decay constant; for t Time nuclides i Nuclide density; The decay power; It is fission energy; To capture energy; S204: Calculate the neutron flux density at the initial moment, and construct the relationship between equation (1) and equation (2) as follows: (6) In the formula: This represents the true value of the neutron flux density at the initial moment; Thermal power; The decay power at the initial moment; The fission energy at the initial moment, The capture energy at the initial moment; S205: Calculate the neutron flux density at the current time step: (7) In the formula: This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides i Nuclide density; nuclide i The recoverable energy from each fission; nuclide i The single-group fission cross section; S206: Calculate the time-integral average of the neutron flux density at the current burnup step, i.e., construct an explicit equation relating the neutron flux density to the burnup step: (8) In the formula: The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. This represents the current time step.

[0007] Preferably, in S5, the iterative form of constructing the neutron flux density includes the following steps: S501: Under constant power In this model, the construct (7) is as follows: (9) (10) In the formula: Z represents the current nuclide. i The number of protons; A is the mass number of the current nuclide; This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides i Nuclide density; nuclide i The single-group fission cross section; S502: Under constant power In this mode, the explicit equations for neutron flux density and burnup step size are applied in... Taylor expansion is performed continuously: (11) In the formula: This represents the neutron flux density at the current time step. Thermal power;k It is the order; S503: The explicit equation for neutron flux density versus burnup step size after Taylor expansion, integrally averaged at the current burnup step size: (12) In the formula: ; The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. S504: with The rigorous expression for neutron flux density is used to construct an iterative form, i.e., a theoretical model for burnup step division: (13) In the formula: ; This is an iterative form of neutron flux density; The actual neutron flux density at the current time step; Thermal power; The decay power; It is fission energy; To capture energy.

[0008] Preferably, in S7, the time integral averaging of the neutronics parameters at the current burnup step includes the following steps: S701: Calculate the time integral average of power at the current fuel consumption step size: (14) in ; Thermal power; The decay power; This is an iterative form of neutron flux density; It is fission energy; To capture energy.

[0009] The present invention has the following beneficial effects: This invention presents a transport-burnup coupling computation method based on adaptive burnup step size partitioning. The method first performs high-fidelity transport-burnup coupling computation to construct explicit equations for neutron flux density and burnup step size, and then estimates the optimal step size using a convergence criterion. Next, iteratively integrating and averaging the neutron flux density yields a theoretical model for burnup step size partitioning, and the optimal step size is obtained through the convergence criterion. Finally, based on the convergence criterion, the assumption of constant neutron parameters within this step size is determined to meet the computational accuracy requirements. Furthermore, based on the theoretical model of burnup step size partitioning, the impact of the step size on computational accuracy can be quantified based on the burnup calculation results of the optimal step size and a custom step size. This invention can adaptively partition the burnup step size within the lifetime while ensuring computational accuracy, reducing the number of burnup steps and transport calculations within each step size, thereby significantly improving the efficiency of transport-burnup coupling computation. Attached Figure Description

[0010] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0011] Figure 1 This is a flowchart of a transport-fuel coupling calculation method based on adaptive fuel consumption step size division according to the present invention.

[0012] Figure 2 This is a schematic diagram of the MOX fuel cell structure.

[0013] Table 1 shows the results of high-fidelity calculation and adaptive step-size calculation for MOX fuel cells when the burnup depth ranges from 0.5 GWd / tU to 70 GWd / tU. k inf and its relative error. Detailed Implementation

[0014] The present invention will be further described in detail below through specific embodiments. These embodiments are intended to enable those skilled in the art to gain a more comprehensive understanding of the present invention, but do not limit the invention in any way.

[0015] This embodiment uses the MOX fuel cell benchmark published by JAEA, which has a constant power output of 37.0 W / gU, a uniform step size of 0.5 GWd / tU, and a final burnup depth of 70 GWd / tU. The geometric model is as follows: Figure 2 As shown, the system comprises three material-filled regions: fuel, cladding, and moderator, from the inside out. The calculation program used was the independently developed fuel consumption calculation program AMAC, and the fuel consumption database used was a simplified fuel consumption chain provided by JENDL, including 21 heavy nuclei, 49 fission products, and 1 pseudonucleus.

[0016] like Figure 1As shown, the transport-fuel consumption coupling calculation method based on adaptive fuel consumption step size provided in this embodiment is performed according to the following steps: The first step is to obtain the fission energy, capture energy and decay energy of each nuclide based on evaluation databases such as ENDF / B-VIII.0 and JENDL-5. The second step establishes the relationship between thermal power and usable energy power as follows: (1) In the formula: Thermal power; This refers to the fission power. The decay power; For capturing power; The third step is to solve the burnup equation to obtain the required neutron flux density. The neutron flux density is calculated after converting thermal power into usable energy. The relationship between thermal power and available energy is as follows: (2) In the formula: Thermal power; The decay power; Neutron flux density; For fission energy, To capture energy; The fourth step involves inputting the fission energy, capture energy, and decay energy of each nuclide obtained from the database for each available energy level to obtain the following: (3) (4) (5) In the formula: , , They are nuclides i The recoverable energy from each fission, capture, and decay; , , Different nuclides i Single-group fission, trapping cross section, and decay constant; for t Time nuclides i Nuclide density; The decay power; It is fission energy; To capture energy; Fifth, calculate the neutron flux density at the initial moment and construct the relationship between equation (1) and equation (2) as follows: (6) In the formula: This represents the true value of the neutron flux density at the initial moment; Thermal power; The decay power at the initial moment; The fission energy at the initial moment, The capture energy at the initial moment; Step 6: Calculate the neutron flux density at the current time step: (7) In the formula: This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides i Nuclide density; nuclide i The recoverable energy from each fission; nuclide i The single-group fission cross section; Step 7: Calculate the time-integral average of the neutron flux density at the current burnup step size, i.e., construct an explicit equation relating the neutron flux density to the burnup step size: (8) In the formula: The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. This represents the current time step.

[0017] Step 8: Determine the custom burnup step size based on the explicit equation of neutron flux density and burnup step size; Step 9: Determine if the current step size satisfies the rough estimate of the optimal step size for fuel consumption calculation. If the current fuel consumption step size does not reach the rough estimate of the optimal step size, then adjust the step size and proceed to step seven; If the current fuel consumption step size reaches the rough estimate of the optimal step size, then proceed to step ten; Step 10, at constant power In this model, the construct (7) is as follows: (9) (10) In the formula: Z represents the current nuclide. i The number of protons; A is the mass number of the current nuclide; This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides iNuclide density; nuclide i The single-group fission cross section; Step 11, at constant power In this mode, the explicit equations for neutron flux density and burnup step size are applied in... Taylor expansion is performed continuously: (11) In the formula: This represents the neutron flux density at the current time step. Thermal power; k It is the order; Step 12: Integrate and average the explicit equations for neutron flux density versus burnup step size after Taylor expansion, at the current burnup step size: (12) In the formula: ; The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. Step thirteen, with The rigorous expression for neutron flux density is used to construct an iterative form, i.e., a theoretical model for burnup step division: (13) In the formula: ; This is an iterative form of neutron flux density; The actual neutron flux density at the current time step; Thermal power; The decay power; It is fission energy; To capture energy.

[0018] Step 14: Determine if the current step size satisfies the optimal step size for fuel consumption calculation. If the current fuel consumption step size has not reached the optimal step size, adjust the step size and proceed to step thirteen. If the current fuel consumption step size reaches the optimal step size, proceed to step fifteen; Step 15: Calculate the time integral average of power at the current fuel consumption step size: (14) in ; Thermal power; The decay power; This is an iterative form of neutron flux density; It is fission energy; To capture energy.

[0019] Step sixteen: Determine whether the constant neutronics parameters within this burnup step meet the computational accuracy requirements. If the neutronics parameters remain constant within the current burnup step and the required calculation accuracy is not met, then adjust the step size and proceed to step seven. If the neutronics parameters remain constant within the current burnup step and meet the required calculation accuracy, then output the current burnup step and end the current calculation.

[0020] Figure 2 This is a schematic diagram of the MOX fuel cell structure.

[0021] Table 1 shows the combustion calculation method of MOX fuel cells at different combustion depths in this invention based on adaptive combustion step size partitioning. k inf And its relative error. High-fidelity calculation and adaptive step-size calculation are used respectively. High-fidelity calculation requires 141 fuel consumption steps throughout the entire lifespan, while adaptive step-size calculation divides the fuel consumption step into 31 steps throughout the lifespan, which greatly reduces the frequency of transport-fuel consumption coupling calculation.

[0022] Table 1. Different burn depths k inf and its relative error

[0023] Although the preferred embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many specific modifications under the guidance of the present invention without departing from the spirit of the invention and the scope of protection of the claims, and these modifications all fall within the scope of protection of the present invention.

Claims

1. A transport-fuel coupling calculation method based on adaptive fuel consumption step size partitioning, characterized in that, Includes the following steps: S1: Based on the evaluation database, obtain the fission energy, capture energy and decay energy of each nuclide; S2: Based on thermal power and available energy conversion, construct explicit equations for neutron flux density and burnup step size; S3: Determine the custom burnup step size based on the explicit equation of neutron flux density and burnup step size; S4: Determine if the current step size satisfies the rough estimate of the optimal step size for fuel consumption calculation. If the current fuel consumption step size does not reach the rough estimate of the optimal step size, then adjust the step size and proceed to S3; If the current fuel consumption step size reaches the rough estimate of the optimal step size, then proceed to S5; S5: Pass the current burnup step size and neutron flux density, and construct the iterative form of the neutron flux density; S6: Determine if the current step size satisfies the optimal step size for fuel consumption calculation: If the current fuel consumption step size has not reached the optimal step size, adjust the step size and proceed to S5; If the current fuel consumption step size reaches the optimal step size, proceed to S7; S7: Calculate the time integral average of neutronics parameters at the current fuel consumption step; S8: Determine whether the constant neutronics parameters within the burnup step meet the required computational accuracy. If the neutronics parameters remain constant within the current fuel consumption step and the required calculation accuracy is not met, then adjust the step size and proceed to S3; If the neutronics parameters remain constant within the current burnup step and meet the required computational accuracy, then the current burnup step is output.

2. The transport-fuel coupling calculation method based on adaptive fuel consumption step size partitioning according to claim 1, characterized in that, The evaluation database in S1 uses ENDF / B-VIII.0 or JENDL-5.

3. The transport-fuel coupling calculation method based on adaptive fuel consumption step size partitioning according to claim 1, characterized in that, In S2, an explicit equation is constructed for the neutron flux density and the burnup step size; this includes the following steps: S201: The relationship between thermal power and available energy power is as follows: ；（1） In the formula: Thermal power; This refers to the fission power. The decay power; For captured power; S202: Neutron flux density required to solve the burnup equation The neutron flux density is calculated after converting thermal power into usable energy. The relationship between thermal power and available energy is as follows: ；（2） In the formula: Thermal power; The decay power; Neutron flux density; For fission energy, To capture energy; S203: For each available energy, the fission energy, capture energy, and decay energy of each nuclide obtained from the database are used to obtain: ；（3） ；（4） ；（5） In the formula: , , They are nuclides i The recoverable energy from each fission, capture, and decay; , , Different nuclides i Single-group fission, trapping cross section, and decay constant; for t Time nuclides i Nuclide density; The decay power; It is fission energy; To capture energy; S204: Calculate the neutron flux density at the initial moment, and construct the relationship between equation (1) and equation (2) as follows: ；（6） In the formula: This represents the true value of the neutron flux density at the initial moment; Thermal power; The decay power at the initial moment; The fission energy at the initial moment, The capture energy at the initial moment; S205: Calculate the neutron flux density at the current time step: ；（7） In the formula: This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides i Nuclide density; nuclide i The recoverable energy from each fission; nuclide i The single-group fission cross section; S206: Calculate the time-integral average of the neutron flux density at the current burnup step, i.e., construct an explicit equation relating the neutron flux density to the burnup step: ；（8） In the formula: The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. This represents the current time step.

4. The transport-fuel coupling calculation method based on adaptive fuel consumption step size partitioning according to claim 1, characterized in that, In S5, the iterative form of constructing the neutron flux density includes the following steps: S501: Under constant power In this model, the construct (7) is as follows: ；（9） ； （10） In the formula: Z represents the current nuclide. i The number of protons; A is the mass number of the current nuclide; This represents the neutron flux density at the current time step. Thermal power; for t Time nuclides i Nuclide density; nuclide i The single-group fission cross section; S502: Under constant power In this mode, the explicit equations for neutron flux density and burnup step size are applied in... Taylor expansion is performed continuously: ；（11） In the formula: This represents the neutron flux density at the current time step. Thermal power; k It is the order; S503: The explicit equation for neutron flux density versus burnup step size after Taylor expansion, integrally averaged at the current burnup step size: ； （12） In the formula: ; The average neutron flux density within the current time step; This represents the neutron flux density at the current time step. S504: with The rigorous expression for neutron flux density is used to construct an iterative form, i.e., a theoretical model for burnup step division: ； （13） In the formula: ; This is an iterative form of neutron flux density; The actual neutron flux density at the current time step; Thermal power; The decay power; It is fission energy; To capture energy.

5. The transport-fuel coupling calculation method based on adaptive fuel consumption step size partitioning according to claim 1, characterized in that, In S7, the time integral averaging of the neutronics parameters at the current burnup step includes the following steps: S701: Calculate the time integral average of power at the current fuel consumption step size: ； （14） in ; Thermal power; The decay power; This is an iterative form of neutron flux density; It is fission energy; To capture energy.

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